Outlier handling of Robust Geographically and Temporally Weighted Regression

Geographically and temporally weighted regression (GTWR) is an expansion of geographically weighted regression involving elements of time in modeling. This method produces a model that is local to each location and time so that the resulting model is more representative. In the GTWR analysis, the regression coefficient estimates are calibrated by the weighted least squares procedure, but the estimates are not robust against the outliers. In fact, if there are outliers in the data, it may create fictitious structures in the estimates of the coefficients which may mislead the result. By using a robust regression with M-estimator developed in GTWR modeling and applied on the number participants of family planning in East Java from 2009 to 2016, it can be concluded that the modeling of the robust GTWR with M-estimator can overcome the problem of outliers that occurred at the location and time studied. These are indicated by the change in the direction of the parameter estimator coefficients which are more relevant with the data plot, the fitted values that are closer to the actual value and a decrease in the MAD value in the model.